Closed-Loop Identification of Two-Input Two-Output Critically Damped Second-Order Systems with Delay

A closed-loop identification method is proposed for the identification of two-input two-output (TITO) critically damped second-order plus time delay (CSOPTD) systems. The method proposed by Dhanya Ram and Chidambaram [Closed Loop Reaction Curve Method for Identification of TITO Systems, IFAC Proceedings Volume IFAC–Paper On line, 3 (2014)] for the identification of first-order plus time delay model parameters of TITO systems is extended to identify CSOPTD parameters of a higher order model. The responses are compared with the response curve given by Clark [Control System Dynamics. Cambridge University Press (2005)] for a third-order system. From this, the values of K, τe and ζ for the closed-loop response are identified for the third-order system. The interactions are identified as third-order systems using an optimization method, as no standard method has been reported for the identification of the interactions. The initial guess values for this are obtained from the Yuwana and Seborg [“A New Method for On-line Controller Tuning”, AIChE J., 28, pp. 434–440 (1982)] method. From the closed responses and interactions, the open-loop transfer functions are modelled as a CSOPTD model using the relationship between the open-loop model and closed-loop model. Better model fitting is obtained using the proposed method. The effect of measurement noise on the identification of the model is also studied.